Multidimensional Lévy White Noise in Weighted Besov Spaces

In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrability properties of the noise using the indices introduced by Blumenthal, Getoor, and Pruitt. Our techniques rely on wavelet methods and generalized moments estimates for Lévy noises.


Published in:
Stochastic Processes and Their Applications, 127, 5, 1599–1621
Year:
2017
Publisher:
Amsterdam, Elsevier
Keywords:
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 Record created 2017-04-06, last modified 2018-03-17

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